Triangle LMN is isosceles with LM = LN; X and Y are points on LM, LN respectively such that LX = LY. Prove that triangles LMY and LNX are congruent.

1. are the triangles similar and if so why? what is the value of x? show your work.

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis.y = 7ex, y = 7e^-x, x = 1; about the y-axis

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 12611261 chips and a standard deviation of 118118 chips. (a) determine the 2626th percentile for the number of chocolate chips in a bag. (b) determine the number of chocolate chips in a bag that make up the middle 9696% of bags. (c) what is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?